Monday, September 12, 2011

Randomness and the Laws of Physics: Quotes from "MetaMath" by Gregory Chaitin

For those of you that were following my series of posts on the source of the directionality of time and the post on Godel's Incompleteness Theorem, I thought that you'd be interested in the following quotes from a book by Gregory Chaitin called "MetaMath." I'm going to just copy down the quotes, and then make a quick summary at the end. If you're interested in starting a discussion, write a comment, and I'll expand on my thoughts about the book.


"Since you can always fit an equation through a set of data (even random data), then question is: How do we decide if the universe is capricious or if science actually works?
And here's Leibniz's answer: If the laws has to be extremely complicated, then the points are placed at random. But if the law is simple, then it's a genuine law of nature; we're not fooling ourselves!"


"The laws of physics (as written in binary form) must be smaller in length than the data they try to fit."

"A number with infinite precision, a so-called real number, is actually rather unreal!
Most real numbers are transcendental, and hence not computable.
Why should I believe in a real number if I can't calculate it?"

 "So what would be really nice [in a computer program] is to be able to obtain more intelligence, or a higher degree of consciousness, than you yourself possess! You, who set up the rules of the [software] universe in the first place."



"Turing: Halting Problem implies Incompleteness
Turing: Uncomputability implies Incompleteness
My Approach: Randomness implies Incompleteness"

"Mathematical truth has infinite complexity, even though any [set of mathematical axioms] only has finite complexity. In fact, even the world of Diophantine problems has infinite complexity, no finite [set of mathematical axioms] will do. I therefore believe that we cannot stick with a single [set of axioms], as Hilbert wanted, we've got to keep adding new axioms, new rules of inference, or some other kind of new mathematical information to the foundations of our theory. And where can we get new stuff that cannot be deduced from we already know? Well, I'm not sure, but I think that it may come from the same place that physicists get their new equations: based on inspiration, on imagination and on experiments.
No mechanical process (rules of the game) can be really creative, because in a sense anything that ever comes out was already contained in your starting point. Does this mean that physical randomness, coin tossing, something non-mechanical, is the only possible source of creativity?! At least from this (enormously over-simplified!) point of view, it is."

In many ways, Chaitin's statements above are similar to what I was discussing in the post on left-right assymmetry and Godel's Incompleteness Theorem. Life somehow is faced with axioms that it doesn't know whether to accept as 'true' or 'false.'  A few examples are "Do the angles of a triangle add up to 180 degrees?" or "Should we use left-handed amino-acids for right-handed amino-acids?"
And this is similar to what I've been saying in my posts about the directionality of time. In order to have a directionality to time, you need a law of physics that can introduce randomness. It appears that this force is the weak nuclear force, since it is the only force that is not time or space reversible, i.e. there is no symmetry operator with regard to spatial or time reflection.
If I am understanding Chaitin correctly, there can only be creativity if there is a source of randomness. I know that this sounds absurd, but it appears that the reason that the world is not deterministic is due to interactions involving the weak nuclear force.
Let me know what you think.

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